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Chapter 3: Symbolic Manipulation 63
03SYMBOL.DOC TI-89/TI-92 Plus: Symbolic Manipulation (English) Susan Gullord Revised: 02/23/01 10:52 AM Printed: 02/23/01 2:12 PM Page 63 of 24
When
Exact/Approx = AUTO
, the
TI
-
89 / TI
-
92 Plus
uses exact rational
arithmetic wherever all of the operands are rational numbers.
Otherwise, floating-point arithmetic is used after converting any
rational operands to floating-point. In other words, floating-point is
“infectious.” For example:
1/2
−
1/3
transforms to
1/6
but
0.5
−
1/3
transforms to
.16666666666667
This floating-point infection does not leap over barriers such as
undefined variables or between elements of lists or matrices. For
example:
(1/2 - 1/3) x + (0.5
−
1/3) y
transforms to
x/6 + .16666666666667 y
and
{1/2 - 1/3, 0.5
−
1/3}
transforms to
{1/6, .16666666666667}
In the
AUTO
setting, functions such as
solve
determine as many
solutions as possible exactly, and then use approximate numerical
methods if necessary to determine additional solutions. Similarly,
‰
(integrate)
uses approximate numerical methods if appropriate
where exact symbolic methods fail.
Advantages Disadvantages
You see exact results
when practical, and
approximate numeric
results when exact
results are impractical.
You can often control
the format of a result by
choosing to enter some
coefficients as either
rational or floating-point
numbers.
If you are interested only in exact
results, some time may be wasted
seeking approximate results.
If you are interested only in approximate
results, some time may be wasted
seeking exact results. Moreover, you
might exhaust the memory seeking those
exact results.
AUTO
Setting